Individual differences on General speed

.title[
# Individual differences on General speed
]
.subtitle[
## An outline for 2nd year exam
]
.author[
### Adriana F. Chávez De la Peña
]
.institute[
### Lee Lab; Fall 2022
]
.date[
### October 14, 2022
]

---

# Outline

**PART 1.** The study of individual differences

**PART 2.** Individual differences in Cognitive control

**PART 3.** General Speed and the study of reaction times

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# Part 1: The study of individual differences

Differential Psychology

Reliability

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## Differential Psychology

**Experimental research:**

- **Focus:** Identifying systematic variations in performance of groups or experimental conditions.
  
--
  
- ANOVA-based

- Maximize within-subject variance **(Reduce between-subject variance)**

**Differential research:**

- **Focus:** How do people differ from one another?

- Correlation-based.

- **Maximize between-subjects variance**

---

## Reliability

- An experimental effect is reliable to the extent that it consistently replicates across studies and labs.

- A measure is reliable as long as it rank-orders individuals across measurements

The closer the performance observed across participants.

… the better, for an experimental researcher.

… the worse, for a differential researcher.

Robust experimental effects do not necessarily imply reliable individual differences.

---

### Logie et al., 1996

**Study on:**

The reliability of the **word-length effect** and the **phonological-similarity effect** on **auditory/visual stimuli** during a serial order recall task.

**First experiment:**  (N=251)

- Strong aggregate effects (group mean differences),

- Only 57% of the subjects showed all effects of interest at the individual level.

**Retest: ** (N=40)

- Robust effects at the aggregate level.

- Low correlations (r = 0.1 - 0.3) across experiments.

- **Whether a subject showed the effect in the initial test was not predictive of their performance on retest.**

---

# Part 2: Individual differences in Cognitive control

Overall definition and tasks

Difference Scores

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# Defining Cognitive Control

The ability to ignore irrelevant information and suppress automatic responses.

**EXAMPLE:** Stroop task

- YELLOW

- GREEN

- RED

- BLUE

**Two experimental conditions:** Congruent / Incongruent

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## Cognitive Control tasks

### Flanker task

---

## Cognitive Control tasks

### Global/Local task

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../../../Pictures/globalLocal_incongruent.png" alt="Andres and Fernandes, 2006" width="50%" />
Andres and Fernandes, 2006
</div>

---

## Cognitive Control tasks

### Simon task

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../../../Pictures/simonnnnn.png" alt="Kharitonova et al. (2013)" width="95%" />
Kharitonova et al. (2013)
</div>

---

## Cognitive Control tasks

### Antisaccade

<div class="figure" style="text-align: center">
<img src="data:image/png;base64,#../../../Pictures/antisaccade.png" alt="Everling and Fischer (1998)" width="50%" />
Everling and Fischer (1998)
</div>

---

# Measuring Cognitive Control

In general, cognitive control tasks incorporate a distinction between a **condition that requires inhibition** and a **condition that does not require inhibition**

- Incongruent trials

- Congruent trials

The focus is on the comparison of the performance observed across conditions.

- Performance is characterized by the **response times** observed.

Tasks designed to study cognitive control often rely on **Donders' subtraction method**

---

## Donders' subtraction method (1868)

- "Mental operations" take time and do not occur simultaneously.

- Distinctive mental processes can be isolated by subtracting the **mean response time** observed across different conditions.

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# Difference scores

`$$\Huge Y_i = \bar{\mbox{RT}_{\mbox{In}}}-\bar{\mbox{RT}_{\mbox{Co}}}$$`

---

- What can we learn about one person's cognitive control from these difference scores?

- Can we predict performance on task B from the score observed on task A?

- What are the **individual differences in cognitive control**?

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## Individual differences in Cognitive Control

**Rey-Mermet et al., 2019**

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## Data sets explored

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# Correlations across difference scores

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## Big debate: Is there such a thing as cognitive control?

1. **Yes**, cognitive control is a robust cognitive process, (Miyake-Friedman, 2004)

- Cognitive control is a key component of executive functions.

- Cognitive control may not be unidimensional, but it can be
broken down into clear components (inhibition to prepotent
responses / resistancce to interference)

2. **No**, inhibition control is more of an umbrella term,
(Rey-Mermet,2018; Xiao,2022)

- These are all "task-specific" processes.

- There’s a complex interplay between sensory inputs, motor outputs, and task demands.

---

## Difference Scores as a problematic measure

`$$\Huge \rho_{dd'} = \frac{\rho_{xx'}-\rho_{xy}}{1-\rho_{xy}}$$`

(Draheim et al., 2019)

Let's assume...

...Individual components have perfect reliability ( `$\Large \rho_{xx'}=1$` )

...Individual components are independent from each other ( `$\Large \rho_{xy}=0$` )

**The reliability of difference scores is attenuated**

As `$\Large \rho_{xy}$` increases, the reliability of the resulting difference scores decreases

---

## Difference Scores as a problematic measure

- Donders' subtraction method relies on **the isolation** of latent cognitive processes

- High correlations between incongruent and congruent RT are expected.

- It is expected to have shared systematic variance across incongruent and congruent RTs.

- Subtracting one of them from the other removes the systematic variance, leaving only the error variance.

---

## Factorial structure of overall RT

**Rey-Mermet et al., 2019**

---

## Factorial structure of Difference scores

**Rey-Mermet et al., 2019**

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## Arguments against Difference Scores

- “Differences between scores are much more unreliable than the scores themselves” (Lord, 1956).

- “Scores formed by subtracting pretest scores from postest scores lead to fallacious conclusions, primarily because such scores are systematically related to any random error of measurement” (Cronbach and Furby, 1970)

- “Difference scores have low convergent validity caused by deficiencies in test-retest reliability” (Paap & Sawi, 2016)

**Overall:** Difference scores are particularly problematic for **differential** studies.

---

## Sequential congruency effect

- Interference effects are smaller when preceded by another trial of high interference, and larger when preceded by a congruent trials, (Gratton, Coles, & Donchin, 1992).

- Measured by the difference between two interference effects.

- Whitehead et al. (2018) report low even–odd split half reliabilities for sequential congruency effects observed across three tasks (.07 to .17), each of which showed strong effects at the aggregate level.

---

## Alternatives to Difference Scores

- Using pure RT instead of Difference Scores (Kane et al., 2016; McVay and Kane, 2012)

- Switching to Accuracy metrics doesn’t reduce complications.

- To develop a new metric that merges RTs with Accuracy (Draheim et al., 2016, Vandierendonck, 2017; Vandierendonck, 2018)

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## Binning scores (Draheim et al., 2016)

Step 1: Compute mean RT for **correct congruent trials**. (X)

Step 2: Subtract X from every **correct incongruent trials**. (Y)

Step 3: Order all Y values across subjects from lower to largest, and assign a score from 1 to 10 to scores on each decile. (Z)

Step 4: For incorrect incongruent trials, assign an arbitrary Z value of 20 (Z).

Step 5: Compute individual bin scores by adding Z values.

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# Part 3: General Speed

Correlations across General Speed

RT in the literature

RT distribution analysis

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## Correlations across general speed

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## Correlations across General speed

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##  Correlations across difference scores

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# Factorial structure of general speed

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## Factorial structure of difference scores

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## Precedents

- Paap and Sawi (2016) report test–retest reliabilities across executive functioning tasks that rely on difference scores (N=81). Pure RT reliabilities were higher (.71–.89), than difference scores (.43–.62).

- Salthouse et al. (1998) report split-half reliabilities for a task switching paradigm (N=100) that were lower at the level of the difference scores (0.61) than the general RT component (0.91)

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## Problems associated with using RT

**RTs are sensitive to speed-accuracy manipulations**

- Higher ability individuals are more likely to slow down to prevent errors, (Draheim et al.,  2016).

- Unsworth et al., (2012) report no correlation between posterror slowing adjustments and working memory capacity across four cognitive control tasks.

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## Problems associated with using RT

**RTs are impure**

`$$\Large \mbox{RT}_k = (A+B+C)\times G_k + B \times \Delta_k + R_k + E_k$$`

(Miller and Ulrich, 2013)

- Correlations among pure RTs are uninformative

**Paradox:** Difference scores mitigate the impurity issue

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##  RT distribution analysis

- Long-standing tradition in Psychology (Hohle, 1965; Ratcliff, 1978)

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##  RT distribution analysis

- Long-standing tradition in Psychology (Hohle, 1965; Ratcliff, 1978)

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## RT distribution analysis

- **Foundation:** Properties of the RT distribution observed capture latent aspects of human cognition.

- Move away from analysis that consider only RT means or medians.

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## The Worst performance rule

- Slowest RTs are more indicative of general intelligence than the faster RTs.

Larson and Alderton, 1990

- If individual RTs are ranked and grouped into RT bands, the median RT observed in lower bands have stronger correlations with measures of general intelligence and WM.

Robust finding (Coyle, 2003)

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## Ex-Gaussian distribution

`$$\Large Y_{i} \sim \mbox{Normal}(\mu+\tau_i,\sigma^2)$$`
`$$\Large \tau_i \sim \mbox{Exp}(\nu)$$`

**Theoretical interpretations** (Hohle, 1965)

- Gaussian component reflects peripheral sensory-motor and automatic processes

- Exponential component characterizes central, decision-making related processes.

- Exponential component `$\tau$` seems to be a good predictor of working memory and intelligence, (Schmiedek et al., 2007).

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# Our research

- To explore the unifactorial structure identified across Rts (general speed)

- Conduct RT distribution analysis to explore whether this unifactorial structure can be traced back to individual parameters.

- In doing so, we will use a Cognitive Latent Variable modeling approach.

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# Thank you!